In this paper we address the problem of low-authority controller (LAC) design.
The premise is that the actuators have limited authority, and hence cannot
significantly shift the eigenvalues of the system. As a result, the closed-loop
eigenvalues can be well approximated analytically using perturbation theory.
These analytical approximations may suffice to predict the behavior of the
closed-loop system in practical cases, and will provide at least a very strong
rationale for the first step in the design iteration loop. We will show that
LAC design can be cast as convex optimization problems that can be solved
efficiently in practice using interior-point methods. Also, we will show that
by optimizing the l1 norm of the feedback gains, we can arrive at sparse
designs, i.e., designs in which only a small number of the control gains are
nonzero. Thus, in effect, we can also solve actuator/sensor placement or
controller architecture design problems.